1. Field of the Invention
This invention relates to apparatus and methods to estimate refractive power of the human cornea, and to apparatus and methods to reshape the human cornea based on the estimation. More particularly, it relates to techniques to closely model the human cornea to accurately estimate the current refraction and determine a desired corneal shape.
2. Background of Related Art
Current refractive systems calculate estimates of the refractive power of the human cornea and reshape the human cornea based on these refractive errors. The devices that estimate the refractive power of the human cornea are known as corneal topographers. These devices normally use spherical models of the eye to report the refractive power of the cornea. The devices that reshape the human cornea are known as photo polishing systems. An exemplary system is the LaserSight LSX laser system. This device uses a small beam (nominal 1 mm) and a relatively high repetition rate (100 Hz or greater) to remove tissue from the human cornea and reshape it as desired. The combination of the small spot size and x-y scanning controls allows for fine control of the corneal tissue removed.
Both topography systems and photo polishing systems require a model of the human cornea to determine the current refractive power of a patient""s cornea, and/or to determine a target ablated corneal surface. The current techniques for estimation of corneal shape use spherical, toric, meridional variation, or conicoid models of the cornea. Depending on which model is chosen, differing estimations of corneal refraction can be obtained.
The first model used for the human cornea was a sphere. Work by Charles R. Munnerlyn, Ph.D in xe2x80x9cProtorefractive keratectomy: A technique for laser refractive surgeryxe2x80x9d, Journal Cataract and Refractive Surgery, vol. 14, Jan. (1988), shows that if the initial shape of the human cornea could be modeled as a sphere, then the tissue to remove to target the ideal refractive shape is the intersection with a different sphere that is determined by the refraction. The technique to determine this second sphere is a direct consequence of Snell""s law of refraction and the measured corneal index of refraction. When using this model to determine the material to remove for the desired corneal refractive power, the difference between this model and the real shape of the human cornea can create known errors such as induced spherical aberration. Additionally, this technique is only applicable to treatments that are of constant refractive correction across the entire surface because it is radially symmetric. This model is not appropriate for people with any type of astigmatism.
The second technique used to model the cornea is based on a torus. A torus will compensate for the spherical models limitations. With this model, curvatures along a major and minor axis which are constant along their respective axes can be estimated. Current contact and eyeglass technology uses toric lenses. This model can be used for topographic estimation of the refractive power of the human cornea or as a basis for planning tissue removal to go from an initial to a final refractive power of a cornea.
However, a known problem with this technique is that the fit does not account for spherical aberration. Moreover, terms or parameters which are required to specify such a torus are radius of curvature along the major and minor axes and the rotation E for alignment of the axis.
To address the issue of human corneal modeling while accounting for spherical aberrations, the use of meridional variation and conicoid surfaces were explored. For instance, a paper by Kiely (i.e., Kiely, P.M. xe2x80x9cThe mean shape of the human corneaxe2x80x9d. Optica Acta, 1982, Vol. 29, No. 8, pp 1024-1040) demonstrates the usefulness of aspheric corneal shapes. The conicoid presented by Kiely may be described best as a prolate or oblate spheroid. This class of shapes are spheres that have been either flattened or stretched along a single axis.
Kiely further disclosed that the nominal stretching of the human cornea uses a Q parameter of xe2x88x920.26 (xc2x10.18). This fitting model requires a further parameter over the basic spherical corneal model that includes a Q value.
A typical equation that models a conicoid was described, e.g., by George Smith in xe2x80x9cConstruction, Specification, and Mathematical Description of Aspheric Surfacesxe2x80x9d, American Journal of Optometry and Physiological Optics, vol. 60, No. 3, pp. 216-223 (1983). Such a conicoid equation can be written as:
x2+y2+(1+Q)z2xe2x88x922zR=0xe2x80x83xe2x80x83(1)
Equation (1) is a good model for the human corneas, but generally only so long as the cornea is rotationally symmetric about the pupil or optical axis of the eye. However, this model does not fit well for people with corneal astigmatism, a very common ailment among corneal reshaping patient""s.
To account for corneal astigmatism, Kiely proposed the use of a meridional variation surface. This surface is generated by defining a minor and major axis angle and refractive power, and parametrically determining all other values as a function of these parameters by the following equations:
Q(xcex8)=Q1+Q2cos2(xcex8xe2x88x92xcex1)xe2x80x83xe2x80x83(2)
R(xcex8)=R1+R2cos2(xcex8xe2x88x92xcex1)xe2x80x83xe2x80x83(3)
In equations (2) and (3), Q1, Q2, and R1, R2 are the major and minor axis Q values, and radii of curvature (refractive power along the axis), respectively. The values of xcex1 and xcex2 specify the angles containing the maximum and minimum value of Q and R, respectively.
The conicoid does provide a reasonable result, but generally only when used as a basis for removing tissue that does not introduce artifacts. Artifacts relate to the recognition that the difference between two conicoids is continuous, whereas the difference between two meridional variable surfaces is not. However, it does not allow for astigmatic treatment types. The meridional variation surface closely models the astigmatic corneal surface, but using it as a basis for tissue removal introduces artifacts that are based upon the properties of this surface type.
There is thus a need for an ablation laser system and method which utilizes accurate ellipsoidal modeling for precise and realistic refractive correction of corneas.
In accordance with one aspect of the present invention, a corneal surface estimation modeler comprises a corneal measurement input module to receive corneal measurement information regarding a patient""s cornea, and an ellipsoid fitter to generate a best fit ellipsoid to the corneal measurement information relating to a corneal surface of the patient""s cornea.
A method of ablating corneal tissue in accordance with another aspect of the present invention comprises modeling a patient""s cornea with a best-fit ellipsoid, comparing the best-fit ellipsoid with an ideal ellipsoid, and determining a difference between the best-fit ellipsoid and an ideal ellipsoid.